Should anyone need references to support use of FIsher's LSD with k = 3 groups, here are a few.

• Baguley T. Serious stats: A guide to advanced statistics for the behavioral sciences. Macmillan International Higher Education; 2012 Jun 26.
• Howell DC. Statistical methods for psychology. Cengage Learning; 2012.
• Meier U. A note on the power of Fisher's least significant difference procedure. Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry. 2006 Oct;5(4):253-63.

From Thom S Baguley's book (2012, p. 495), and with J representing the number of independent groups:

"The LSD procedure protects against Type I errors only through the omnibus ANOVA test. It is unusual in this respect (because most popular procedures are not conditional on an earlier test). With large values of J it should be avoided, as it provides only weak control of Type I error. However, when J = 3 it is effective at controlling both the rate and number of Type I errors (and, because the individual tests are uncorrected, it maximizes statistical power for a given level of α)."

I agree with Steve

I don't agree :)

Fisher's LSD keeps the family-wise error-rate in the strong sense at alpha if:

1) there are 3 groups (allowing 3 different pairwise comparisons),

2) the individual H0's are tested only when ANOVA p < alpha, and

3) the 3 individual H0's are rejected at alpha

Jochen Wilhelm, let me see if I follow. Point 2 is true when the null hypo is true only alpha% of the time (with usual assumptions). Doesn't this mean anything done in step 3 cannot increase this probability above alpha?

Yes, when H0 is true, the probability that the ANOVA p < alpha is just alpha (I would't turn this into a frequency; it's a probability). Your conclusion is correct if you think about the FWER in the weak sense (weakcontrolof the FWER). This is true for any number of groups.

But if you assume that the ANOVA H0 is false, you expect to reject it - and then the door isopen to accumulate type-I errors (assuming not all group means are different). This means that the FWER is not controlled in the strong sense -- except there are just 3 groups.

Usually, the assumption of the ANOVA H0 is not really sensible, particularily not when the aim is to look for pair-wise differences. It is thus usually not interseting if one is able to reject the ANOVA H0, except for this very special case of Fisher's LSD. Usually one would use a post-hoc test that is not "ANOVA-protected" (and forget the ANOVA altogether). (The ANOVA, or testing ANOVA H0's is useful if one wants to compare nested linear models; unfortunately, "one df-cases" are then also identical to "t-tests")

Should anyone need references to support use of FIsher's LSD with k = 3 groups, here are a few.

• Baguley T. Serious stats: A guide to advanced statistics for the behavioral sciences. Macmillan International Higher Education; 2012 Jun 26.
• Howell DC. Statistical methods for psychology. Cengage Learning; 2012.
• Meier U. A note on the power of Fisher's least significant difference procedure. Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry. 2006 Oct;5(4):253-63.

From Thom S Baguley's book (2012, p. 495), and with J representing the number of independent groups:

"The LSD procedure protects against Type I errors only through the omnibus ANOVA test. It is unusual in this respect (because most popular procedures are not conditional on an earlier test). With large values of J it should be avoided, as it provides only weak control of Type I error. However, when J = 3 it is effective at controlling both the rate and number of Type I errors (and, because the individual tests are uncorrected, it maximizes statistical power for a given level of α)."